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Questions concerning Decoherence and Entanglement 
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#1
Jan3007, 10:24 PM

P: 36

Hello, I have two questions I wish to ask concerning Decoherence and entanglement:
1. I am certainly no expert on quantum mechanics, and while I was reading I stumbled upon the concept of decoherence. I understand the idea, but I have a few questions concerning it: 1. theoretically, if the environment "slows down," similar to entering a state of low energy, can a particle that is entangled still produce interferences? 2. Assuming that a system is always changing in some way, does interference completely cancel out? 3. Do particle interferences arise faster than the speed of light (assuming the entangled system is not dissipative)? I also have a few questions concerning entanglement: 1. Is entanglement permanent within a system? 2. Is everything in the universe entangled? 3. If the above is true, then why are there are so much differences between the states of all systems? 4. How and which properties are usually correlated? 5. Is there "antientanglement"? Thanks for all who answer my quick questions. 


#2
Feb207, 06:17 PM

P: 36

I am astounded. Does no one know the answers to my questions?



#3
Feb207, 06:30 PM

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PF Gold
P: 29,239

One of the things we learn in physics is that the questions that we asked must be clearly defined, or else we would not know what to look for. Concepts and ideas in physics have clearly, underlying mathematical definition. This means that in particular cases, there are certain welldefined description of things such as "entanglement", "energy of the system", etc.. When you use that in a mixandmatch way without knowing the "rules" in which they can be used, then you can easily end up with something that do not make sense or has no clear definition. Questions like these typically either have no answers, or have varying answers depending on how a reader interprets the question. This means that you'll end up with a bunch of different answers based on different premises, and that can only mean a jumbled mess. I'm guessing that most people on here have encountered the latter scenario on here and simply have no "energy" to be involved in another one. I know I am. Zz. 


#4
Feb207, 10:05 PM

P: 36

Questions concerning Decoherence and Entanglement
By "changing in some way" I meant that: If a entangled system exhibited change in any way, (any variable from spin to energy), is there any possibility of interferences manifesting? So, are you suggesting there is no paradigm that describes decoherence or that my langauge in expressing my questions is too ambiguous? I apologize if my language did not make sense earlier. 


#5
Feb307, 05:09 AM

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PF Gold
P: 29,239

I think I still need to do creative interpretation here.
Zz. 


#6
Feb307, 07:53 PM

P: 36

I don't know anything about decoherence destroying entanglement, as such, I thought entanglement is something that was forever standing. Could you explain? Thanks. 


#7
Feb407, 05:05 AM

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PF Gold
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Zz. 


#8
Feb407, 10:06 AM

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PF Gold
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If we look at an entangled threesome, then we the quantum interference effects are only visible in the 3rd order correlation functions between measurements on the 3 components: the individual measurements look like those of mixtures, and so do the second order correlations: they look like statistical mixtures. Now, with entanglement with the environment, we've LOST the control over all the components of the system, as they are myriads, and of different nature. So, the entanglement with the environment leads us to see a system as just a statistical mixture, with no interference effects (limited to the system) left. As such, the entanglement with the environment has the effect upon the system, locally, of suppressing all forms of observable interference. As with the EPR pair, one should *in principle* be able to find "strange correlations" between measurements on the system and on ALL the entangled components of the environment, but these observations are practically impossible. So we NEVER see such "strange correlations", and conclude that the quantum superposition has been transformed into a statistical mixture (but that's only because the correlation has now been promoted to such highorder and unmeasurable correlation function, that we never notice). So "uncontrolled entanglement" promotes quantum interference to highn correlation functions which are totally unobservable for all practical purposes. The individual systems which get entangled with the environment loose hence all form of "coherence" by themselves. 


#9
Feb407, 11:56 AM

P: 36

I don't really know what you mean by statistical mixture. So, what how it comes to me, it seems like you are stating that entangled systems DO NOT correlate observables but, for some reason, interference doesn't exist. Isn't this the opposite of entanglement, if pieces of a system just fail to make correlation with each other? Also, is there any way to figure out why systems collapse superposition if there is no entanglement in the sense of the EPR pair? Thanks for answering the first of my questions. I hope to see more answers too. 


#10
Feb507, 02:18 AM

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For a pure beam, all photons are in a single quantum state (a vector in hilbert space). For a mixture, they are, well, coming in a statistical mixture of different pure states (although this expression, by itself, needs some caveats  but not all difficulties at once ) The point is that observational differences between different "states" are only visible when doing statistical measurements on a big number of "identical" systems. So we're talking here about the observational difference between the components of an entangled system (read: on a whole series of such systems, or a beam of such particles in this case), and those that aren't. Quantum theory's only reason of existence is that there are states in nature which seem to be DIFFERENT from simple statistical mixtures, so the "quantumness" of an observation is the difference between such mixture and the quantum predictions. In short: there's a difference between the quantum state: psi> = a> + b>  which is a pure state on one hand (sheer "quantumness") and: a statistical mixture of 50% of things coming in in state a> and 50% of things coming in in state b>. But you only see the difference if you do 2 things: 1) you do observations on MANY of these "identical" systems 2) you look at the right quantities. For instance: if you look at a property which is determined by state a> or by state b> (in other words, if a> and b> are eigenvectors of the measurement operator), both cases 1) and 2) will give identical results. IOW, we haven't seen any "quantum effect" when doing that. However, if you look at a quantity which is determined by c> and d>, where c> = a> + b> and d> = a>  b>, you WILL see a difference: in case 1), in 100% of the cases, you will see the cproperty and never the dproperty ; while in case 2), you will find 50% of cproperty and 50% of dproperty. It is in this kind of case, where you find a difference between a pure state and a statistical mixture, that you can say you have observed a "quantum effect" or "quantum interference" or something of the kind. Well, in the case of entangled systems, these observations showing such effects need to be measurements on ALL components of the entangled system: if you miss one, it turns out like if it were a statistical mixture. IF you observe them, they are very puzzling. But if the entanglement is too complicated, you always leave out one necessary measurement on some part of the system, and hence you don't see any quantum effect: everything behaves as a mixture. So although there "are" very puzzling quantum effects to be potentially observed, you can never actually do so when there is entanglement with the environment ; and hence things appear to be "just statistical mixtures" with no quantum effects per se. This is the essential idea of decoherence theory. Now, in the case of an EPR pair, we can go and do observations on the single other partner in the entanglement, and find amazing correlations. But if it is not a pair, but a billionsome, then there will always be one partner that escapes observation. And it is only on the total set of observations that a correlation (an amazing correlation) is visible. On any subset of observations, the entangled state appears as a mixture. 


#11
Feb507, 10:58 AM

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#12
Feb507, 11:41 PM

P: 36




#13
Feb607, 03:56 AM

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So, for pure states of single particles, the "quantum effect" already resides in an interference pattern (which is the difference between the actual probability density observed/predicted, and that which should have resulted from the pure application of the statistical mixture of the "intuitive" basis). This always happens when the observed state is a pure state in superposition of "intuitive basis states", and when we look at an observation which is NOT that same basis. This comes simply about because of the "absolute square" rule of complex numbers in quantum theory: the fact that if u and v are complex numbers, that u+v^2 = u^2 + v^2 + 2 Re(u.v*) The first two terms is what we obtain also in the the "statistical mixture of the intuitive basis" view, and the last term is the "interference term" which gives us the difference with the quantum prediction. It's all in this last term, and it is THIS term, in all circumstances, which is the entire content of "quantum effects". It is this term which gives us the "interference patterns" in the twoslit experiment. In the EPR setup, the pure state is u>d>  d>u>. The "intuitive basis" is one in which each particle "has its own state", hence spanned by: u>u> ; u>d> ; d>u> and d>d>, and our pure state is clearly a superposition of these "individual particle state" states. THIS kind of superposition is called an "entangled state", btw: when "individual states of the subsystems" are considered to be the "intuitive basis", and when the state is not in just one of those. So in this case, we will only see possible "interference effects" as compared to a statistical mixture of "intuitive basis states", when we do a measurement which is NOT one with an eigenbasis equivalent to the "intuitive basis" ; in other words, it will need to be a correlation measurement, which has eigenstates NOT of the kind u>d>,... Measurements ONLY affecting one subsystem WILL have such an eigenbasis corresponding to the intuitive basis, and hence in those measurements, the "quantum effects" will not show up. 


#14
Feb607, 11:43 PM

P: 36

Also, if subsystems' quantum effects do not show up, then why do they 'appear' in, say, the double slit experiment? I think I am missing something with interference, outside of its definition of wavesuperposition. To me, you seem to be speaking of a different kind of superposition. Could you continue to explain on this? Thanks again. 


#15
Feb707, 02:20 AM

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The point is that in order to see quantum effects, you have to "prepare" a subsystem, followed by a "measurement". If you do raw measurements on a subsystem which is entangled with other stuff, you will not see any "interference" at all, because the subsystem will appear to you as being part of a statistical mixture. However, if you prepare (filter !) a subsystem, you will be able again, to see interference. But the preparation is ALSO a kind of measurement! As such, the observed quantum effect is nothing else but a correlation between two successive measurements (the preparation, followed by the actual measurement). If, between both, you do not have any interactions which might "decohere" (read: entangle) your subsystem with anything else, then these correlations may show up. 


#16
Feb807, 11:52 PM

P: 36

One thing I am understanding is the idea of having a 'pure state' being a different state that is an 'interference pattern.' If this is so, is the eigenstate not a 'pure' state, or is that just a consequence of the HUP, that as more information is known the lesserknown properties become more 'unknown'? And, in relation to this statement: " In the EPR setup, the pure state is u>d>  d>u>. The "intuitive basis" is one in which each particle "has its own state", hence spanned by: u>u> ; u>d> ; d>u> and d>d>, and our pure state is clearly a superposition of these "individual particle state" states. THIS kind of superposition is called an "entangled state", btw: when "individual states of the subsystems" are considered to be the "intuitive basis", and when the state is not in just one of those." Does that mean that entanglement is nothing more than the 'strange state' or the term 'entangled state' just part of the terminology used. It is because of uses of the term 'entanglement' that leads me to suspect that it is something a bit different from "correlating observables." It's probably my ego, but can you clarify this? So, what I have gotten so far is that measuring any system with a 'intuitive basis,' finding certain eigenvalues of the system, will result in quantum interferences of some kind. And when we don't measure something, the system is in a superposition of 'intuitive states.' Finally, can you give a different example of 'interferences,' because my mind is confused about what they really are in a quantum system outside of a 'wavepatter' in the double slit experiment. Thanks for bearing with my questions. I hope to receive more answers 


#17
Feb907, 02:56 AM

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An "eigenstate" is of course always a pure state, and I really really don't see what the HUP is doing in this. So, given that I cannot understand exactly what you ask and how you see things, I have no way of trying to give an explanation that might make any sense to you. I can try to write some elementary statements, but I don't know if they are related to what you are asking/saying. 1) "pure states" are quantum states which are vectors in hilbert space. We talk about an individual specimen, but we think in fact about an entire beam of such specimen. They are such, that there exists a complete set of observables (= a set of compatible measurements) for which ALL systems in that beam give exactly the same results to all of these measurements. There is, in other words, no statistical spread in the outcomes, and the system behaves completely deterministically. Mind you that you don't have the choice about WHICH observables to pick. For instance, a particle can be in a pure state, which happens to be a position state. A beam of such particles will then yield ALWAYS THE SAME RESULT when we do position measurements X, Y and Z on them. But a particle can be also in another pure state, which happens to be a momentum state. In that case, a beam of such particles will ALWAYS GIVE THE SAME OUTCOMES when we do a momentum measurement (but not when we do a position measurement!). So we see that a pure state is somehow associated with a set of observables for which the outcomes will be determined with certainty, but it is the state which determines the observables. We don't have the choice. For most pure states, however, these observables are only theoretical, and are not really realizable as a measurement in the lab (although they could, in principle). The set of all these possible pure states span the hilbert space of quantum states. But we can also think of a beam of particles, of which not all of them are in the same pure state, but which are statistically mixed. One might be in a position state , the next might be in a momentum state, etc... In such a case, we say that the beam (and by extrapolation, each individual in the beam) is "in a mixture". A beam in a mixture is such, that there doesn't exist, even in theory, any complete set of observables for which the outcome is always the same. We will ALWAYS have a statistical spread of outcomes, no matter what kind of measurement we do. This wasn't the case for a beam in a pure state: there, there existed at least ONE COMPLETE SET of measurements for which the outcomes would always be the same. However, if we apply, to a beam in a pure state, a set of measurements, which is not the "good" set, then we have ALSO a statistical distribution of outcomes. So if we limit us to such measurements, we're not really making a difference between "a statistical mixture" and "a pure state". Quantum effects typically show up when: 1) in an "intuitive set of measurements" we seem to have a mixture 2) in a specific set of measurements which are not so intuitive, we "always find the same result". Because of 1), one would be tempted to think of the beam as "just being a statistical mixture of stuff", and then 2) is entirely puzzling, because 2) cannot happen for a GENUINE statistical mixture of stuff. Almost all (if not all) "paradoxes" in quantum theory can be reduced to such a scheme. The point is that, because they are nevertheless pure states, that there are "funny outcomes" of certain measurements, which are not compatible with the mixture we might think is there, if we look upon it in the "intuitive basis". 


#18
Feb1007, 11:57 PM

P: 36

If I may ask one more question: how does this all tie into Bell's theorem and nonlocality/acasaulity? I'm just getting curious... 


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